A uniformly charged solid sphere of radius R has potential V ₀ (measured with respect to infinity) on its surface. For this sphere the equipotential surfaces with potentials 3 ~V ₀ 2 , V ₀ 1 , 3 ~V ₀ 4 and V ₀ 4 have radius R ₁, R ₂, R ₃ and R ₄ and respectively, then

Step-by-step solution

The potential V(r) of a uniformly charged solid sphere of radius R and total charge Q is given by: V(r) = kQ R = V₀ for r R V(r) = kQ r for r > R Given V(R) = V₀ , we have V₀ = kQ R . For r R , the potential is constant at V₀ . Since 3V₀ 2 > V₀ , no point inside or on the surface has this potential. Thus, R₁ does not exist or is not defined in the physical sense of the sphere, but the option R₁=0 is often used in such contexts to denote the impossibility of the condition. However, checking the potential values: V₀